A Special Class Of Permutation Polynomials

Niederreiter in 1991 proposed an open problem-to characterize polynomials in n indeterminates over a finite field F_q which are permutation polynomials over every finite extension of F_q. Qifan Zhang studied it for the case n=2 and solved the problem under the condition gcd((?)f/(?)x, (?)f/(?)y)=1 and Deg(f)(?)0 (modp), here p is the characteristic of F_q. In this paper the author obtains the same result with the condition replaced by gcd((?)f/(?)x,(?)f/(?)y)=1 and gcd(deg_xf, deg_yf)(?)0 (mod p).